Rewrite as a simplified fraction. ${0.7\overline{8} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 78.8888...\\ 10x &= 7.8888...\end{align*}}$ Subtracting the two equations, we have: ${90x = 71}$ ${x = \dfrac{71}{90}} $